The formal errors on the Gaia EDR3 parallaxes are modestly underestimated, according to recent publications. For example, [1]} investigated the completeness, accuracy, and precision of the EDR3 catalog. They calculate the unit weight uncertainties of the catalog, which are the factors by which the formal errors must be increased to represent the true level of uncertainty. The multiplicative factor is only around 1.2 for most stars, although it can rise to a factor of more than 2 in the worst cases. Further, the errors have been shown to be most significantly underestimated for brighter stars [2]}. Unfortunately, many of the Milky Way field Cepheids used for distance determinations lie in this very bright apparent magnitude range, with our own sample having magnitudes between \(4<G<11\)  mag. Additionally, Cepheids vary dramatically in temperature over their cycle, averaging about 1000K from maximum to minimum light [3]}, corresponding to a peak-to-peak color variation of about 0.5 mag in the optical region. Since the Gaia parallax offset is known to vary with magnitude and color, this could introduce larger parallax errors for individual Cepheids. [4]} state that the pipeline for variable stars has significantly improved since DR2; however, since the color of a star is still assumed to be the same in all observations, corrections for the chromaticity may not be fully accurate, so there are still issues to be solved in future data releases.
